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Re: NDSolve Method?

  • To: mathgroup at
  • Subject: [mg3438] Re: NDSolve Method?
  • From: Sebastian Bauer <bauer at>
  • Date: Thu, 7 Mar 1996 02:24:41 -0500
  • Organization: Institute B for Mechanics, TU Muenchen, GERMANY
  • Sender: owner-wri-mathgroup at

I have kept an Article from John Fultz (WRI Technical Support) about
this question:

Article: 1024 of comp.soft-sys.math.mathematica
>From: John Fultz <jfultz at>
>To: mathgroup at
>Subject: Re: [mg1604] NDSolve algorithm

According to the Mathematica FAQ on the Web


NDSolve uses an Adams Predictor-Corrector method for non-stiff
differential equations and backward difference formulas (Gear method)
for stiff differential equations. It switches between the two methods
using heuristics based on the adaptively selected step size. It starts
with the non-stiff method under essentially all conditions, and checks
for the advisability of switching methods every 10 or 20 steps.

The algorithms and the heuristics for switching between algorithms are
described in the following references:

     Alan C. Hindmarsh, "ODEPACK: A Systematized Collection of ODE
     Solvers", in Scientific Computing, R. S. Stepleman et. al. (eds).
     North-Holland, Amsterdam (1983), pp. 55-64.

     Linda R. Petzold, "Automatic Selection of Methods for Solving
     Stiff and Nonstiff Systems of Ordinary Differential Equations",
     SIAM Journal of Scientific and Statistical Computing, 4 (1983),
     pp. 136-148.
This methods were originally used for the FORTRAN ode-solver
package ODEPACK (public available on NETLIB).

I hope, that covers what you wanted to know.

Dipl.-Ing. Sebastian Bauer <bauer at>
Institute B for Mechanics, Technical University of Munich
Luisenstrasse 37a, 80290 Muenchen
phone: (001-49) 89 - 2105 3204, FAX: (001-49) 89 - 2105 3209


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